Solve (x+2y)^2-(x+y)(x-3y)-5y^2

$$( x + 2 y ) ^ { 2 } - ( x + y ) ( x - 3 y ) - 5 y ^ { 2 }$$

Evaluate

$$2y\left(3x+y\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2y\right)^{2}.

$$x^{2}+4xy+4y^{2}-\left(x+y\right)\left(x-3y\right)-5y^{2}$$

Use the distributive property to multiply x+y by x-3y and combine like terms.

$$x^{2}+4xy+4y^{2}-\left(x^{2}-2xy-3y^{2}\right)-5y^{2}$$

To find the opposite of x^{2}-2xy-3y^{2}, find the opposite of each term.

$$x^{2}+4xy+4y^{2}-x^{2}+2xy+3y^{2}-5y^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$4xy+4y^{2}+2xy+3y^{2}-5y^{2}$$

Combine 4xy and 2xy to get 6xy.

$$6xy+4y^{2}+3y^{2}-5y^{2}$$

Combine 4y^{2} and 3y^{2} to get 7y^{2}.

$$6xy+7y^{2}-5y^{2}$$

Combine 7y^{2} and -5y^{2} to get 2y^{2}.

$$6xy+2y^{2}$$

Expand

$$6xy+2y^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2y\right)^{2}.

$$x^{2}+4xy+4y^{2}-\left(x+y\right)\left(x-3y\right)-5y^{2}$$

Use the distributive property to multiply x+y by x-3y and combine like terms.

$$x^{2}+4xy+4y^{2}-\left(x^{2}-2xy-3y^{2}\right)-5y^{2}$$

To find the opposite of x^{2}-2xy-3y^{2}, find the opposite of each term.

$$x^{2}+4xy+4y^{2}-x^{2}+2xy+3y^{2}-5y^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$4xy+4y^{2}+2xy+3y^{2}-5y^{2}$$

Combine 4xy and 2xy to get 6xy.

$$6xy+4y^{2}+3y^{2}-5y^{2}$$

Combine 4y^{2} and 3y^{2} to get 7y^{2}.

$$6xy+7y^{2}-5y^{2}$$

Combine 7y^{2} and -5y^{2} to get 2y^{2}.

$$6xy+2y^{2}$$